Properties

Label 166635bf
Number of curves $2$
Conductor $166635$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("bf1")
 
E.isogeny_class()
 

Elliptic curves in class 166635bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
166635.x1 166635bf1 \([0, 0, 1, -101568, 38542014]\) \(-1073741824/5325075\) \(-574672312268556075\) \([]\) \(1824768\) \(2.0921\) \(\Gamma_0(N)\)-optimal
166635.x2 166635bf2 \([0, 0, 1, 898242, -943371387]\) \(742692847616/3992296875\) \(-430841345224016671875\) \([]\) \(5474304\) \(2.6415\)  

Rank

sage: E.rank()
 

The elliptic curves in class 166635bf have rank \(1\).

Complex multiplication

The elliptic curves in class 166635bf do not have complex multiplication.

Modular form 166635.2.a.bf

sage: E.q_eigenform(10)
 
\(q - 2 q^{4} - q^{5} - q^{7} + 3 q^{11} - 4 q^{13} + 4 q^{16} - 6 q^{17} + q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.